30 citations · 253 across the 53 of their papers we have counts for
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A Unified Analysis on the Subgradient Upper Bounds for the Subgradient Methods Minimizing Composite Nonconvex, Nonsmooth and Non-Lipschitz Functions
Daoli Zhu, Lei Zhao, Shuzhong Zhang
This paper presents a unified analysis for the proximal subgradient method (Prox-SubGrad) type approach to minimize an overall objective of , subject to convex constrain…
Spectrally Constrained Optimization
Casey Garner, Gilad Lerman, Shuzhong Zhang
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to…
An Augmented Lagrangian Approach to Conically Constrained Non-monotone Variational Inequality Problems
Lei Zhao, Daoli Zhu, Shuzhong Zhang
In this paper we consider a non-monotone (mixed) variational inequality model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like p…
Beyond Monotone Variational Inequalities: Solution Methods and Iteration Complexities
Kevin Huang, Shuzhong Zhang
In this paper, we discuss variational inequality (VI) problems without monotonicity from the perspective of convergence of projection-type algorithms. In particular, we identify ex…
Efficient First Order Method for Saddle Point Problems with Higher Order Smoothness
Nuozhou Wang, Junyu Zhang, Shuzhong Zhang
This paper studies the complexity of finding approximate stationary points for the smooth nonconvex-strongly-concave (NC-SC) saddle point problem: . Under the s…
An Accelerated Variance Reduced Extra-Point Approach to Finite-Sum VI and Optimization
Kevin Huang, Nuozhou Wang, Shuzhong Zhang
In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum hemivariational inequality (HVI) problem. In this HVI problem, the associated fun…
An Approximation-Based Regularized Extra-Gradient Method for Monotone Variational Inequalities
Kevin Huang, Shuzhong Zhang
In this paper, we propose a general extra-gradient scheme for solving monotone variational inequalities (VI), referred to here as Approximation-based Regularized Extra-gradient met…
Cubic-Regularized Newton for Spectral Constrained Matrix Optimization and its Application to Fairness
Casey Garner, Gilad Lerman, Shuzhong Zhang
Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then…
A Gradient Complexity Analysis for Minimizing the Sum of Strongly Convex Functions with Varying Condition Numbers
Nuozhou Wang, Shuzhong Zhang
A popular approach to minimize a finite-sum of convex functions is stochastic gradient descent (SGD) and its variants. Fundamental research questions associated with SGD include: (…
Minimax Problems with Coupled Linear Constraints: Computational Complexity, Duality and Solution Methods
Ioannis Tsaknakis, Mingyi Hong, Shuzhong Zhang
In this work we study a special minimax problem where there are linear constraints that couple both the minimization and maximization decision variables. The problem is a generaliz…
Primal-Dual First-Order Methods for Affinely Constrained Multi-Block Saddle Point Problems
Junyu Zhang, Mengdi Wang, Mingyi Hong +1
We consider the convex-concave saddle point problem , where the decision variables and/or subj…
New First-Order Algorithms for Stochastic Variational Inequalities
Kevin Huang, Shuzhong Zhang
In this paper, we propose two new solution schemes to solve the stochastic strongly monotone variational inequality problems: the stochastic extra-point solution scheme and the sto…
Linearly-Convergent FISTA Variant for Composite Optimization with Duality
Casey Garner, Shuzhong Zhang
Many large-scale optimization problems can be expressed as composite optimization models. Accelerated first-order methods such as the fast iterative shrinkage-thresholding algorith…
A Unifying Framework of Accelerated First-Order Approach to Strongly Monotone Variational Inequalities
Kevin Huang, Shuzhong Zhang
In this paper, we propose a unifying framework incorporating several momentum-related search directions for solving strongly monotone variational inequalities. The specific combina…
Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures
Derek Singh, Shuzhong Zhang
This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantell…
A First-Order Primal-Dual Method for Nonconvex Constrained Optimization Based On the Augmented Lagrangian
Daoli Zhu, Lei Zhao, Shuzhong Zhang
Nonlinearly constrained nonconvex and nonsmooth optimization models play an increasingly important role in machine learning, statistics and data analytics. In this paper, based on…
Generalization Bounds for Stochastic Saddle Point Problems
Junyu Zhang, Mingyi Hong, Mengdi Wang +1
This paper studies the generalization bounds for the empirical saddle point (ESP) solution to stochastic saddle point (SSP) problems. For SSP with Lipschitz continuous and strongly…
On Lower Iteration Complexity Bounds for the Saddle Point Problems
Junyu Zhang, Mingyi Hong, Shuzhong Zhang
In this paper, we study the lower iteration complexity bounds for finding the saddle point of a strongly convex and strongly concave saddle point problem: . We…
An Optimal High-Order Tensor Method for Convex Optimization
Bo Jiang, Haoyue Wang, Shuzhong Zhang
This paper is concerned with finding an optimal algorithm for minimizing a composite convex objective function. The basic setting is that the objective is the sum of two convex fun…
Adaptive Stochastic Variance Reduction for Subsampled Newton Method with Cubic Regularization
Junyu Zhang, Lin Xiao, Shuzhong Zhang
The cubic regularized Newton method of Nesterov and Polyak has become increasingly popular for non-convex optimization because of its capability of finding an approximate local sol…
A Unified Adaptive Tensor Approximation Scheme to Accelerate Composite Convex Optimization
Bo Jiang, Tianyi Lin, Shuzhong Zhang
In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization mo…
A Cubic Regularized Newton's Method over Riemannian Manifolds
Junyu Zhang, Shuzhong Zhang
In this paper we present a cubic regularized Newton's method to minimize a smooth function over a Riemannian manifold. The proposed algorithm is shown to reach a second-order -s…
An ADMM-Based Interior-Point Method for Large-Scale Linear Programming
Tianyi Lin, Shiqian Ma, Yinyu Ye +1
We propose a new framework to implement interior point method (IPM) to solve very large linear programs (LP). Traditional IPMs typically use Newton's method to approximately solve…
Accelerating Adaptive Cubic Regularization of Newton's Method via Random Sampling
Xi Chen, Bo Jiang, Tianyi Lin +1
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assum…